Parity-time Symmetry Research Articles

On the Limitations of the Coupled Mode Theory and Parity-Time Symmetry for Near-Field Wireless Power Transfer Research

On the Limitations of the Coupled Mode Theory and Parity-Time Symmetry for Near-Field Wireless Power Transfer Research

Parity-time symmetry enabled ultra-efficient nonlinear optical signal processing

Nonlinear optical signal processing (NOSP) has the potential to significantly improve the throughput, flexibility, and cost-efficiency of optical communication networks by exploiting the intrinsically ultrafast optical nonlinear wave mixing. It can support digital signal processing speeds of up to terabits per second, far exceeding the line rate of the electronic counterpart. In NOSP, high-intensity light fields are used to generate nonlinear optical responses, which can be used to process optical signals. Great efforts have been devoted to developing new materials and structures for NOSP. However, one of the challenges in implementing NOSP is the requirement of high-intensity light fields, which is difficult to generate and maintain. This has been a major roadblock to realize practical NOSP systems for high-speed, high-capacity optical communications. Here, we propose using a parity-time (PT) symmetric microresonator system to significantly enhance the light intensity and support high-speed operation by relieving the bandwidth-efficiency limit imposed on conventional single resonator systems. The design concept is the co-existence of a PT symmetry broken regime for a narrow-linewidth pump wave and near-exceptional point operation for broadband signal and idler waves. This enables us to achieve a new NOSP system with two orders of magnitude improvement in efficiency compared to a single resonator. With a highly nonlinear AlGaAs-on-Insulator platform, we demonstrate an NOSP at a data rate approaching 40 gigabits per second with a record low pump power of one milliwatt. These findings pave the way for the development of fully chip-scale NOSP devices with pump light sources integrated together, potentially leading to a wide range of applications in optical communication networks and classical or quantum computation. The combination of PT symmetry and NOSP may also open up opportunities for amplification, detection, and sensing, where response speed and efficiency are equally important.

In-plane elastic waves in piezoelectric metamaterials with Parity–Time symmetry

The propagation of in-plane waves in piezoelectric metamaterial involves the coupling of longitudinal (i.e. quasi–pressure), transverse (i.e. quasi–shear) and electric potential waves, which can result in different exotic phenomena. In this study, the stiffness matrix method is used to analyze the dispersion relation, which contains anomalous propagation characteristics. With the coupling of electric potential, the frequency spectrum of in–plane wave shows new characteristics. The exceptional point caused by non–Hermitian operator that does not exist before also appears when the vertical wave number is imaginary. The oblique incidence of the in–plane wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes which include the negative refraction. The normal mode decomposition is developed to study the in-plane incidence of piezoelectric metamaterial and then the averaged Poynting vector is applied to obtain the refraction angle. Moreover, the defect layer is introduced into the phononic crystals to study the transmission coefficients with two different symmetrical arrangements. When the balanced gain and loss are considered in the metamaterial, the Parity–Time symmetry appears and brings in pairs of exceptional points to achieve a complete transmission with a unidirectional zero reflection.

Gap solitons in quasi-1D Bose–Einstein condensate with three-body interactions under PT symmetry

The existence and stability of gap solitons in a quasi-one-dimensional Bose–Einstein condensate with three-body interactions loaded in a PT-symmetric potential are investigated numerically. Under the mean-field approximation, the dynamical behaviors of the system are described by a cubic-quintic Gross–Pitaevskii equation. Firstly, we obtained the band-gap structures via linearizing the GPE. The PT-symmetric of the system will be broken if the magnitude of the imaginary part of the external potential exceeds a critical value. Secondly, various of gap solitons were found by the Newton-Conjugate-Gradient method. Finally, the stability properties of gap solitons were investigated through the linear stability analysis and the direct long-time nonlinear dynamical evolution. The results indicated that the stability of on-site and off-site solitons was remarkably influenced by three-body interactions. There exists unstable on-site gap solitons when the PT-symmetric potential is taken into account. Additionally, the magnitude of the imaginary part of the potential also affects the profile and stability of the gap solitons. When it increases, the symmetry of the solitons will be broken.

Topological phases and non-Hermitian topology in tunable nonreciprocal cyclic three-mode optical systems

We propose a method for simulating a 1D non-Hermitian Su-Schrieffer-Heeger model with modulated nonreciprocal hopping using a cyclic three-mode optical system. The current system exhibits different localization of topologically nontrivial phases, which can be characterized by the winding number. We find that the eigenenergies of such a system undergo a real-complex transition as the nonreciprocal hopping changes, accompanied by a non-Bloch parity-time symmetry breaking. We explain this phase transition by considering the evolution of saddle points on the complex energy plan and the ratio of complex eigenenergies. Additionally, we demonstrate that the skin states resulting from the non-Hermitian skin effect possess higher-order exceptional points under the critical point of the non-Bloch parity-time phase transition. Furthermore, we investigate the non-Hermitian skin phase transition by the directional mean inverse participation ratio and the generalized Brillouin zone. This work provides an alternative way to investigate the novel topological and non-Hermitian effects in nonreciprocal optical systems.

Advances in Semiconductor Lasers Based on Parity-Time Symmetry.

Semiconductor lasers, characterized by their high efficiency, small size, low weight, rich wavelength options, and direct electrical drive, have found widespread application in many fields, including military defense, medical aesthetics, industrial processing, and aerospace. The mode characteristics of lasers directly affect their output performance, including output power, beam quality, and spectral linewidth. Therefore, semiconductor lasers with high output power and beam quality are at the forefront of international research in semiconductor laser science. The novel parity-time (PT) symmetry mode-control method provides the ability to selectively modulate longitudinal modes to improve the spectral characteristics of lasers. Recently, it has gathered much attention for transverse modulation, enabling the output of fundamental transverse modes and improving the beam quality of lasers. This study begins with the basic principles of PT symmetry and provides a detailed introduction to the technical solutions and recent developments in single-mode semiconductor lasers based on PT symmetry. We categorize the different modulation methods, analyze their structures, and highlight their performance characteristics. Finally, this paper summarizes the research progress in PT-symmetric lasers and provides prospects for future development.

Entanglement dynamics of two non-Hermitian qubits

The evolution of entanglement in a non-Hermitian quantum system may behave differently compared to its Hermitian counterpart. In this paper, we investigate the entanglement dynamics of two coupled and driven non-Hermitian qubits. Through calculating the concurrence of the system, we find that the evolution of the bipartite entanglement manifests two distinct patterns in the parameter space. In the low non-Hermiticity regime, the concurrence oscillates significantly, while in the opposite regime the same quantity would trend to a stable value. We attribute this phenomenon to parity-time ( PT ) symmetry phase transition. We also study the effect of decoherence on the entanglement dynamics. Our work provides a method to stabilize entanglement by exploiting non-Hermiticity.

Stress guides in generic static mechanical metamaterials

Abstract The confinement of waves within a waveguide can enable directional transmission of signals, which has found wide applications in communication, imaging, and signal isolation. Extending this concept to static systems, where material deformation is piled up along a spatial trajectory, remains elusive due to the sensitivity of localized deformation to structural defects and impurities. Here, we propose a general framework to characterize localized static deformation responses in two dimensional generic static mechanical metamaterials, by exploiting the duality between space in static systems and time in one dimensional non-reciprocal wave systems. An internal time-reverse symmetry is developed by the space-time duality. Upon breaking this symmetry, quasi-static load induced deformation can be guided to travel along a designated path, thereby realizing a stress guide. A combination of time-reverse and inversion symmetries discloses the parity-time symmetry inherent in static systems, which can be leveraged to achieve directional deformation shielding. The tailorable stress guides can find applications in various scenarios, ranging from stress shielding and energy harvesting in structural tasks to information processing in mechanical computing devices.

Activating non-Hermitian skin modes by parity-time symmetry breaking

Parity-time (PT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{PT}}}}}}}}$$\\end{document}) symmetry is a cornerstone of non-Hermitian physics as it ensures real energies for stable experimental realization of non-Hermitian phenomena. In this work, we propose PT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{PT}}}}}}}}$$\\end{document} symmetry as a paradigm for designing rich families of higher-dimensional non-Hermitian states with unique bulk, surface, hinge or corner dynamics. Through systematically breaking or restoring PT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{PT}}}}}}}}$$\\end{document} symmetry in different sectors of a system, we can selectively activate or manipulate the non-Hermitian skin effect (NHSE) in both the bulk and topological boundary states. Some fascinating phenomena include the directional toggling of the NHSE, and the flow of boundary states without chiral or dynamical pumping, developed from selective boundary NHSE. Our results extend richly into 3D or higher, with more sophisticated interplay with selective bulk and boundary NHSE and charge-parity (CP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{CP}}}}}}}}$$\\end{document}) symmetry. Based on non-interacting lattices, PT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{PT}}}}}}}}$$\\end{document}-activated NHSEs can be observed in various optical, photonic, electric and quantum platforms that admit gain/loss and non-reciprocity.

Emergent phenomena with broken parity-time symmetry: Odd-order versus even-order effects

Emergent phenomena with broken parity-time symmetry: Odd-order versus even-order effects

Line-wave waveguide engineering using Hermitian and non-Hermitian metasurfaces

Line waves (LWs) refer to confined edge modes that propagate along the interface of dual electromagnetic metasurfaces while maintaining mirror reflection symmetries. Previous research has both theoretically and experimentally investigated these waves, revealing their presence in the microwave and terahertz frequency ranges. In addition, a comprehensive exploration has been conducted on the implementation of non-Hermitian LWs by establishing the parity-time symmetry. This study introduces a cutting-edge dual-band line-wave waveguide, enabling the realization of LWs within the terahertz and infrared spectrums. Our work is centered around analyzing the functionalities of existing applications of LWs within a specific field. In addition, a novel non-Hermitian platform is proposed. We address feasible practical implementations of non-Hermitian LWs by placing a graphene-based metasurface on an epsilon-near-zero material. This study delves into the advantages of the proposed framework compared to previously examined structures, involving both analytical and numerical examinations of how these waves propagate and the underlying physical mechanisms.

Parity-time imbalance induced by balanced gain and loss medium in non-Hermitian photonic crystals

Photonic crystals, including gain and loss materials, show numerous intriguing features than the ordinary photonic crystals. In this work, using the full wave simulation, we numerically investigate the photonic crystals with gain and loss which are satisfying the parity-time (PT) symmetry condition to reveal the effect of PT symmetry on the optical properties of photonic crystals, including the exceptional point, distribution of electromagnetic fields and edge states. This work reveals a novel mechanism of coexistence and competition between topological states and non-Hermiticity in all-dielectric photonic crystals and provides an innovative understanding of non-Hermiticity in topological photonic systems.

Tunable narrow linewidth fiber laser based on parity-time symmetric double rings and variable optical attenuator

A tunable narrow linewidth fiber ring laser based on parity-time (PT) symmetric double rings and variable optical attenuator (VOA) is demonstrated. The laser is composed of a fiber loop mirror (FLM), which creates two coupled rings: the reflective ring and the transmissive ring. The loss of the transmissive ring can be controlled by tuning the VOA, which balances with the gain of the reflective ring. When the PT symmetry is broken, a single-longitudinal-mode (SLM) laser is realized. The laser can be tuned by an optical tunable filter (OTF), and the tuning range is 38 nm, spanning from 1525 nm to 1563 nm. In the whole tuning process, the linewidth of the laser is at the sub-kHz level, and the optical signal to noise ratios (OSNR) is over 53 dB. The fluctuation of wavelength and power are less than 0.02 nm and 0.52 dB in an hour, respectively.

The second-order coherence analysis of number state propagation through dispersive non-Hermitian multilayered structures

To examine the second-order coherence of light propagation of quantum states in arbitrary directions through dispersive non-Hermitian optical media, we considered two sets of non-Hermitian periodic structures that consist of gain/loss unit cells. We show that each batch can satisfy the parity-time symmetry conditions at a distinct frequency. We then varied the gain/loss strength in the stable electromagnetic regime to evaluate the transmittance of N-photon number states through each structure. The results show both sets preserve their antibunching characteristics under specific incident light conditions. Furthermore, s(p)-polarized light exhibits higher (lower) second-order coherence at larger incident angles. In addition, the antibunching features of the transmitted states degrade with an increase in the number of unit cells in multilayered structures for both polarizations.

Improving the Critical Transmission Distance of Inductively Coupled Wireless Power Transfer Having Parity-Time Symmetry

Improving the Critical Transmission Distance of Inductively Coupled Wireless Power Transfer Having Parity-Time Symmetry

Wavelength-Selective Single-Mode Laser by Joint Use of Parity-Time Symmetry and Vernier Effect in Symmetric and Asymmetric Coupled Microrings

Wavelength-Selective Single-Mode Laser by Joint Use of Parity-Time Symmetry and Vernier Effect in Symmetric and Asymmetric Coupled Microrings

Spin-Reorientation-Driven Linear Magnetoelectric Effect in Topological Antiferromagnet Cu_{3}TeO_{6}.

The search for new materials for energy-efficient electronic devices has gained unprecedented importance. Among the various classes of magnetic materials driving this search are antiferromagnets, magnetoelectrics, and systems with topological spin excitations. Cu_{3}TeO_{6} is a material that belongs to all three of these classes. Combining static electric polarization and magnetic torque measurements with phenomenological simulations we demonstrate that magnetic-field-induced spin reorientation needs to be taken into account to understand the linear magnetoelectric effect in Cu_{3}TeO_{6}. Our calculations reveal that the magnetic field pushes the system from the nonpolar ground state to the polar magnetic structures. However, nonpolar structures only weakly differing from the obtained polar ones exist due to the weak effect that the field-induced breaking of some symmetries has on the calculated structures. Among those symmetries is the PT (1[over ¯]^{'}) symmetry, preserved for Dirac points found in Cu_{3}TeO_{6}. Our findings establish Cu_{3}TeO_{6} as a promising playground to study the interplay of spintronics-related phenomena.

Kármán Vortex Street in a spin-orbit-coupled Bose-Einstein Condensate with PT Symmetry

Abstract The dynamics of spin-orbit-coupled Bose-Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street’ is observed in another component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately 0:18, which is less than the stability condition 0:28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin-orbit coupling disrupts symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize Kármán vortex street in the system.

Parity time symmetry all-optical microwave oscillator using a polarization dependent Sagnac loop

An all-optical microwave oscillator based on parity-time symmetry was proposed and experimentally demonstrated. It mainly consists of a big feedback loop, an active small loop and a polarization-dependent Sagnac loop. The microwave seed signal originates from the beating between the continuous wave and the Stokes wave. The function of microwave envelope detection and feedback modulation are implemented through cross gain modulation of two semiconductor optical amplifiers. By employing the parity time symmetry loops and the Vernier effect, the single mode selectivity capability of the oscillator has been enhanced, and a single mode microwave signal with high quality can be generated. In the experiment, a highly quality microwave signal with a frequency of 10.71 GHz was generated. The single side band phase noise can reach −94.1 dBc/Hz@10 kHz and the side mode suppression ratio of the generated microwave signal reaches 41 dB. Compared to the previously reported all-photonic microwave oscillator, the single side band phase noise is improved by 7 dB at a frequency offset of 10 kHz, and by 20 dB at a frequency offset of 100 Hz. The results indicate that our proposed scheme significantly improves the quality of the generated microwave signals.

Giant and tunable photonic spin Hall effect in a parity-time symmetric structure with a Dirac semimetal material

The optical parity-time (PT) symmetry structure can yield unique properties, including periodicity, discreteness, nonlinearity, and so on. However, the component materials in these PT symmetry structures have been primarily restricted by their lack of tunability. Here, by utilizing the external stimulus-dependent optical properties of the Dirac semimetal, we report the theoretical prediction of the large and controllable photonic spin Hall effect in the PT symmetry structure with the slab of the Dirac semimetal. We provide evidence that the PT symmetry structure with the Dirac semimetal exhibits a large spin shift as high as the half of the waist at a certain incident angle, which is the conventionally theoretical upper limit. Due to the exceptional points, the spin shift can be enhanced effectively. Furthermore, we unravel that a small change in the Fermi energy of the Dirac semimetal on the order of 0.01 eV is able to engineer both the magnitude and sign of the spin shift. In particular, there is a transition in the spectrum of the spin shift when we vary the Fermi energy of the Dirac semimetal, where the number of the spin shift peak changes from one to two. Our results reveal the interplay between the light and the PT symmetry structure with the Dirac semimetal, which offers the possibility of developing Dirac semimetal-based spin-dependent photonic devices.